Chronic liver disease has globally risen mainly due to a prevalent hepatitis C virus (HCV) infection rate and an epidemic of obesity. It is estimated by the year 2030, 2.2 billion people around the world will be overweight and 1.1 billion people will be obese. Diabetes and obesity are the main risk factors for the development of the metabolic syndrome and in the liver of non-alcoholic fatty liver disease (NAFLD) which could progress to non-alcoholic fatty steatohepatitis (NASH) related cirrhosis and liver malignancy. At present there is not effective therapy for NASH besides loss of weight and exercise. Furthermore, optimal management of HCC with curative intent includes resection or liver transplantation. Nevertheless, these therapies are limited because the degree of liver dysfunction or the medical conditions at the time of diagnosis and the scarcity of available liver grafts. The role of cellular lipid management and metabolism in human health and disease is taking a center stage. The present overview articulates the current pathophysiology of fatty liver disease under the aging processes, potential biological markers of liver disease diagnosis and progression and future therapies.

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North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate of the U.S. Supreme Court. Given that counties must be split, the North Carolina legislature and courts [Lak02] have provided guidelines that seek to reduce counties split across districts while also complying with the "one person, one vote" criteria. Under these guidelines, the counties are separated into clusters; each cluster holds a number of districts based on its population. Districts may not span clusters, meaning that each cluster forms an independent set of districts in the sense that it can be subdivided into districts without affecting other clusters. In many county clusters, there are more than one district.The guidelines for clustering counties were clarified by the courts in 2015 [Dic15]. In 2017 the districting plans drawn in 2011 for the North Carolina House and Senate were found to be racially gerrymandered. The remedy accounted for the courts' 2015 clustering clarification and redrew some of the clusters and districts for use in the 2018 elections. The enacted set of clusters in both the state House and state Senate were reported to be optimal in that the remedy produced the largest number of county clusters possible while following the outlined procedure. However, no transparent validation of this claim was provided in the public domain.The primary goal of this work is to develop, present, and publicly release an algorithm to optimally cluster counties according to the guidelines set by the court in 2015. We use this tool to investigate the optimality and uniqueness of the enacted clusters under the 2017 redistricting process. We verify that the enacted clusters are optimal, but find other optimal choices. We emphasize that the tool we provide lists all possible optimal county clusterings.We also explore the stability of clustering under changing statewide populations and project what the county clusters may look like in the next redistricting cycle beginning in 2020/2021. In studying the stability of these clusters, we find that their structure may be highly susceptible to small fluctuations in the population; on average approximately one third of the clusters change each year. In addition, we compare the existing guidelines with an alternative interpretation of how counties might be minimally split. As part of this report, we provide code, 1 along with documentation and examples, which may be used by the public to independently verify the North Carolina legislative district clusters during the next redistricting cycle.The report is organized as follows. In Section 1, we lay out the general redistricting problem for North Carolina in light of various laws and legal precedents. We then explain how this leads to the "county clustering" problem and the court-sanctioned procedure for resolving it. In Section 2, we describe our algorithm and give the needed theoretical justification to ensure it produces all of the optim...

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We give an exponential improvement to the diagonal van der Waerden numbers for r ≥ 5 colors.